Introducing a New Hyperchaotic System and Its Physical Realization by Designing an Analog Electronic Circuit

In this paper, based on Liu chaotic system, a novel hyperchaotic system possessing an origin equilibrium point is introduced. To demonstrate the existence of hyperchaos phenomenon in this system, several mathematical criteria are used and discussed. These criteria comprise dissipativity checking, instability proof of the equilibrium point, draw of phase portraits of strange attractor, time responses of state variables, calculation of Lyapunov exponents, extract of fractional dimension and high sensitivity analysis of system’s time responses to initial conditions. It is shown that positive Lyapunov exponents of the introduced system are larger than ones of other hyperchaotic systems. By altering each of the parameters of the system, different types of dynamical behaviors including chaos, limit cycle, quasi periodic and hyperchaos are observed. An analog electronic circuit is designed to realize the hyperchaotic system composed of linear resistors, linear capacitors, operational amplifiers, and analog multipliers. Moreover, the designed nonlinear circuit is simulated by using ORCAD16.6 software. Next, it is physically implemented and tested in our laboratory. Both simulation results and experimental observations depict the occurrence of hyperchaos phenomenon in the designed circuit.